AUBURN – It’s a kind of jail math.

At noon, the Androscoggin County Jail held 137 inmates. The jail has 137 permanent bunks.

A perfect fit? Nope. It’s still overcrowded jail. Some inmates sleep on cots. And officials say they are running out of solutions.

Programs aimed at putting people to work or monitoring them at home – rather than keeping them here, in the county jail – are operating at capacity.

“We haven’t stopped looking for ways to progress,” acting Chief Deputy Eric Samson said. “But have we figured out a way to fix this? No.”

On the minimum security block, a stack of temporary cots sat in the hallway, waiting for new arrivals. One particular cell, designed in the late 1980s to hold two people, had since doubled in capacity to include a steel bed and one of the stackable bunks.

Those bunks, which the guards call “sleds” because of their resemblance to toboggans, have been put to increasing use lately.

Though the jail population was 137 at noon, the number was above 150 only a few hours earlier. It’s always shifting.

In themselves, population numbers are misleading, Jail Administrator John Lebel said.

One might better think of the jail as having several populations: men, women, violent and non-violent.

There are drunks sleeping off benders in holding cells and accused murderers in the maximum security block.

Neither can fill an empty bunk among the minimum security inmates. Officials shuffle people around.

“At 85 percent, we’re full,” said Lt. Jeffrey Chute, the jail’s assistant administrator.

It’s been more than full for a while.

At the start of 2006, some open beds allowed the jail to board inmates here for other jails.

In the first half of the year, the local jail made more than $55,000 by keeping inmates for other counties.

But that money dried up by summer. There were more prisoners here. And in November, there was a new jail, the Two Rivers Regional Jail.

That facility, a cooperative between Sagadahoc and Lincoln counties, drew most of the boarders being offered from other counties.

The revenue is missed.

County Commissioner Helen Poulin has questioned Sheriff Guy Desjardins about the money loss.

Desjardins is planning to make a full report to the three-member commission on Aug. 29.

“Maybe they need to see it on the positive side,” Desjardins said. “I haven’t had to ask for boarding fees yet.”

His budget has no money set aside to send local prisoners to other jails.

In a bind, the Auburn jail might be able to count on goodwill from other counties, Lebel said. But that wouldn’t last.

He worries that his only remaining step might be to ask the Maine Department of Corrections for a variance to get by with the added inmates.

But it’s a step of last resort, Lebel said.

The variance is meant as a temporary measure, particularly while a jail expansion or construction is underway.

None is planned.

Without the state department’s blessing, an overcrowded jail opens itself to costly lawsuits, Lebel said.

Meanwhile, Lebel, Desjardins and others hope to keep the jail running without catastrophe.

The jail has become a more violent place.

Skirmishes between inmates have increased in recent months, Samson said. Meanwhile, the numbers of guards has dipped. With empty positions and summer vacations, the remaining staff has had to work overtime.

“It’s hard to get the jail maintained and clean with that many people, but we do,” Chute said. “We’ll keep the place running.”